Slope Fields Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
For dy/dx=x2dy/dx = x^2, compute slopes at (0,0)(0,0), (1,0)(1,0), (−1,3)(-1,3), (2,5)(2,5).

Solution

  1. 1
    Slope =x2= x^2: (0,0)(0,0): 0; (1,0)(1,0): 1; (−1,3)(-1,3): 1; (2,5)(2,5): 4.

Answer

Slopes: 0,1,1,40, 1, 1, 4.
Slope depends only on xx, so points on the same vertical line have equal slopes.

About Slope Fields

A graphical representation of a first-order DE dydx=f(x,y)\frac{dy}{dx} = f(x, y). At each point (x,y)(x, y) in the plane, draw a short line segment with slope f(x,y)f(x, y). The resulting pattern of segments shows the direction solutions must follow.

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More Slope Fields Examples

Example 1 easy

For [formula], compute slopes at [formula], [formula], [formula], [formula]. Describe the solution f

Example 2 medium

For [formula], find the zero-slope isocline and describe long-term behavior of solutions.

Example 4 medium

A slope field shows solutions curving toward the [formula]-axis from both sides. What can you infer

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